President Barack Obama looks over the shoulder of Hannah Wyman, 11, as she demonstrates her project in the Blue Room, Feb. 7, 2012, during the second annual White House Science Fair. (Pete Souza/The White House)

An astronaut, software engineer, college president and student walk into the White House...and they’re all women.

It’s not a joke. At least it wasn’t Tuesday morning when The White House Council on Women and Girls held a gathering in the Eisenhower Executive Office Building focusing on girls in the science, engineering, technology and mathematics fields.

The audience included Girl Scouts of varying ages, college students, teachers, parents and mentors. All listened as Environmental Protection Agency Administrator Lisa Jackson gave her introductory remarks and as a panel of some of the nation’s most accomplished women in technology spoke about their personal experiences and the challenges women face in pursuing a career in the STEM fields. The panel included Jackson along with astronaut Dr. Cady Coleman, Facebook Director of Engineering Jocelyn Goldfein, Edmonds Community College President Jean Hernandez and Howard University Chapter of Engineers Without Borders President Bianca Bailey.

The panel hit on nearly all of the major points surrounding women and girls in science and math:

— Yes, you can be a pretty, high-heel-wearing cheerleader sorority sister and be a scientist, engineer or mathematician.

But the event wasn’t held merely for the panel. The White House also took the opportunity to introduce a new video featuring the young girls and women who attended the White House Science Fair this past February:

The event did its part to leave the women and girls in the audience with a sense of can-do-anything empowerment, at least judging by the reactions of the event’s attendees — a woman sitting next to me whispered an audible “wow” at one point.

But there’s a wide gap between discussing the problem of recruiting girls — to say nothing of American students in general — to STEM fields and actually doing something about it. Heads of companies in some of the fastest growing sectors of the economy still complain: We’re ready and eager to hire American workers, but we can’t find ones trained to do the jobs we need them to do. That’s because even as women are surpassing men in the number of advanced degrees earned, they’re not getting those degrees in the most sought-after STEM fields, making them ineligible for numerous, highly-paid jobs at companies such as Facebook, Google and Twitter.

Then there’s the question of cost. Not everyone can afford a four-year degree. In light of this, Hernandez highlighted certificate programs and scholarships as a path towards a job in the technology fields for those who either cannot afford or do not want to attend a four-year college.

“You have a right to prepare for interesting work and economic independence,” said Bailey to slow, affirming nods from the audience.

When asked what it would take for someone to be a candidate to work for Facebook’s engineering department, Goldfein said that summer internships and taking the initiative to build something are two ways to distinguish yourself. In advice specifically to girls, many of whom erroneously believe they are not as good at math and science as their male counterparts, Goldfein said, “Don’t psych yourself out.”

Goldfein also came by The Washington Post later Tuesday afternoon to discuss her take on why women steer clear of math and science and what it will take to bring them into the fold.

Goldfein outlines the unique challenge women face, including a factor as simple as timing. Goldfein says she often finds that women discover computer programming later than boys — a challenge she faced, since she started studying computer science her freshman year in college. But she stresses that, for those women (and men) interested in learning computer programming, it’s never too late. She recommends starting with either Python or PHP, and watching the lectures Stanford University, her alma mater, makes available on the iTunes Store or any of the free tutorials available online.

In terms of what she’s looking for in a potential hire, Goldfein says she’s not as interested in credentials so much as the speed with which someone can learn new things, to say nothing of passion. In hiring new engineers, she looks for people who are clearly devoted to the field, rather than those looking for a high-paying job. Taking on internships, launching new products, exploring new coding languages go further than a GPA. Will you be asked difficult technical questions in the interview? Yes. But if you find an entryway into the field through passion, finding the answers should be a welcome challenge.

Disclosure: The Washington Post Co.'s chairman and chief executive, Donald E. Graham, is a member of Facebook's board of directors.

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